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<li><a class="reference internal" href="#">Early stopping of Stochastic Gradient Descent</a></li>
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<p class="admonition-title">Note</p>
<p>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-linear-model-plot-sgd-early-stopping-py"><span class="std std-ref">here</span></a> to download the full example code or to run this example in your browser via Binder</p>
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<div class="sphx-glr-example-title section" id="early-stopping-of-stochastic-gradient-descent">
<span id="sphx-glr-auto-examples-linear-model-plot-sgd-early-stopping-py"></span><h1>Early stopping of Stochastic Gradient Descent<a class="headerlink" href="#early-stopping-of-stochastic-gradient-descent" title="Permalink to this headline">¶</a></h1>
<p>Stochastic Gradient Descent is an optimization technique which minimizes a loss
function in a stochastic fashion, performing a gradient descent step sample by
sample. In particular, it is a very efficient method to fit linear models.</p>
<p>As a stochastic method, the loss function is not necessarily decreasing at each
iteration, and convergence is only guaranteed in expectation. For this reason,
monitoring the convergence on the loss function can be difficult.</p>
<p>Another approach is to monitor convergence on a validation score. In this case,
the input data is split into a training set and a validation set. The model is
then fitted on the training set and the stopping criterion is based on the
prediction score computed on the validation set. This enables us to find the
least number of iterations which is sufficient to build a model that
generalizes well to unseen data and reduces the chance of over-fitting the
training data.</p>
<p>This early stopping strategy is activated if <code class="docutils literal notranslate"><span class="pre">early_stopping=True</span></code>; otherwise
the stopping criterion only uses the training loss on the entire input data. To
better control the early stopping strategy, we can specify a parameter
<code class="docutils literal notranslate"><span class="pre">validation_fraction</span></code> which set the fraction of the input dataset that we
keep aside to compute the validation score. The optimization will continue
until the validation score did not improve by at least <code class="docutils literal notranslate"><span class="pre">tol</span></code> during the last
<code class="docutils literal notranslate"><span class="pre">n_iter_no_change</span></code> iterations. The actual number of iterations is available
at the attribute <code class="docutils literal notranslate"><span class="pre">n_iter_</span></code>.</p>
<p>This example illustrates how the early stopping can used in the
<a class="reference internal" href="../../modules/generated/sklearn.linear_model.SGDClassifier.html#sklearn.linear_model.SGDClassifier" title="sklearn.linear_model.SGDClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.linear_model.SGDClassifier</span></code></a> model to achieve almost the same
accuracy as compared to a model built without early stopping. This can
significantly reduce training time. Note that scores differ between the
stopping criteria even from early iterations because some of the training data
is held out with the validation stopping criterion.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Authors: Tom Dupre la Tour</span>
<span class="c1">#</span>
<span class="c1"># License: BSD 3 clause</span>
<span class="kn">import</span> <span class="nn">time</span>
<span class="kn">import</span> <span class="nn">sys</span>

<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>

<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">linear_model</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">fetch_openml</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
<span class="kn">from</span> <span class="nn">sklearn.utils._testing</span> <span class="kn">import</span> <span class="n">ignore_warnings</span>
<span class="kn">from</span> <span class="nn">sklearn.exceptions</span> <span class="kn">import</span> <span class="n">ConvergenceWarning</span>
<span class="kn">from</span> <span class="nn">sklearn.utils</span> <span class="kn">import</span> <span class="n">shuffle</span>

<span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>


<span class="k">def</span> <span class="nf">load_mnist</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">class_0</span><span class="o">=</span><span class="s1">&#39;0&#39;</span><span class="p">,</span> <span class="n">class_1</span><span class="o">=</span><span class="s1">&#39;8&#39;</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;Load MNIST, select two classes, shuffle and return only n_samples.&quot;&quot;&quot;</span>
    <span class="c1"># Load data from http://openml.org/d/554</span>
    <span class="n">mnist</span> <span class="o">=</span> <span class="n">fetch_openml</span><span class="p">(</span><span class="s1">&#39;mnist_784&#39;</span><span class="p">,</span> <span class="n">version</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>

    <span class="c1"># take only two classes for binary classification</span>
    <span class="n">mask</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">logical_or</span><span class="p">(</span><span class="n">mnist</span><span class="o">.</span><span class="n">target</span> <span class="o">==</span> <span class="n">class_0</span><span class="p">,</span> <span class="n">mnist</span><span class="o">.</span><span class="n">target</span> <span class="o">==</span> <span class="n">class_1</span><span class="p">)</span>

    <span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">shuffle</span><span class="p">(</span><span class="n">mnist</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="n">mask</span><span class="p">],</span> <span class="n">mnist</span><span class="o">.</span><span class="n">target</span><span class="p">[</span><span class="n">mask</span><span class="p">],</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
    <span class="k">if</span> <span class="n">n_samples</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
        <span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:</span><span class="n">n_samples</span><span class="p">],</span> <span class="n">y</span><span class="p">[:</span><span class="n">n_samples</span><span class="p">]</span>
    <span class="k">return</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span>


<span class="nd">@ignore_warnings</span><span class="p">(</span><span class="n">category</span><span class="o">=</span><span class="n">ConvergenceWarning</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">fit_and_score</span><span class="p">(</span><span class="n">estimator</span><span class="p">,</span> <span class="n">max_iter</span><span class="p">,</span> <span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;Fit the estimator on the train set and score it on both sets&quot;&quot;&quot;</span>
    <span class="n">estimator</span><span class="o">.</span><span class="n">set_params</span><span class="p">(</span><span class="n">max_iter</span><span class="o">=</span><span class="n">max_iter</span><span class="p">)</span>
    <span class="n">estimator</span><span class="o">.</span><span class="n">set_params</span><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>

    <span class="n">start</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
    <span class="n">estimator</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>

    <span class="n">fit_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">start</span>
    <span class="n">n_iter</span> <span class="o">=</span> <span class="n">estimator</span><span class="o">.</span><span class="n">n_iter_</span>
    <span class="n">train_score</span> <span class="o">=</span> <span class="n">estimator</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
    <span class="n">test_score</span> <span class="o">=</span> <span class="n">estimator</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span><span class="p">)</span>

    <span class="k">return</span> <span class="n">fit_time</span><span class="p">,</span> <span class="n">n_iter</span><span class="p">,</span> <span class="n">train_score</span><span class="p">,</span> <span class="n">test_score</span>


<span class="c1"># Define the estimators to compare</span>
<span class="n">estimator_dict</span> <span class="o">=</span> <span class="p">{</span>
    <span class="s1">&#39;No stopping criterion&#39;</span><span class="p">:</span>
    <span class="n">linear_model</span><span class="o">.</span><span class="n">SGDClassifier</span><span class="p">(</span><span class="n">n_iter_no_change</span><span class="o">=</span><span class="mi">3</span><span class="p">),</span>
    <span class="s1">&#39;Training loss&#39;</span><span class="p">:</span>
    <span class="n">linear_model</span><span class="o">.</span><span class="n">SGDClassifier</span><span class="p">(</span><span class="n">early_stopping</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">n_iter_no_change</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span>
                               <span class="n">tol</span><span class="o">=</span><span class="mf">0.1</span><span class="p">),</span>
    <span class="s1">&#39;Validation score&#39;</span><span class="p">:</span>
    <span class="n">linear_model</span><span class="o">.</span><span class="n">SGDClassifier</span><span class="p">(</span><span class="n">early_stopping</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">n_iter_no_change</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span>
                               <span class="n">tol</span><span class="o">=</span><span class="mf">0.0001</span><span class="p">,</span> <span class="n">validation_fraction</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>
<span class="p">}</span>

<span class="c1"># Load the dataset</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">load_mnist</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">10000</span><span class="p">)</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">test_size</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span>
                                                    <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>

<span class="n">results</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">estimator_name</span><span class="p">,</span> <span class="n">estimator</span> <span class="ow">in</span> <span class="n">estimator_dict</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
    <span class="nb">print</span><span class="p">(</span><span class="n">estimator_name</span> <span class="o">+</span> <span class="s1">&#39;: &#39;</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s1">&#39;&#39;</span><span class="p">)</span>
    <span class="k">for</span> <span class="n">max_iter</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">50</span><span class="p">):</span>
        <span class="nb">print</span><span class="p">(</span><span class="s1">&#39;.&#39;</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s1">&#39;&#39;</span><span class="p">)</span>
        <span class="n">sys</span><span class="o">.</span><span class="n">stdout</span><span class="o">.</span><span class="n">flush</span><span class="p">()</span>

        <span class="n">fit_time</span><span class="p">,</span> <span class="n">n_iter</span><span class="p">,</span> <span class="n">train_score</span><span class="p">,</span> <span class="n">test_score</span> <span class="o">=</span> <span class="n">fit_and_score</span><span class="p">(</span>
            <span class="n">estimator</span><span class="p">,</span> <span class="n">max_iter</span><span class="p">,</span> <span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span><span class="p">)</span>

        <span class="n">results</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">estimator_name</span><span class="p">,</span> <span class="n">max_iter</span><span class="p">,</span> <span class="n">fit_time</span><span class="p">,</span> <span class="n">n_iter</span><span class="p">,</span>
                        <span class="n">train_score</span><span class="p">,</span> <span class="n">test_score</span><span class="p">))</span>
    <span class="nb">print</span><span class="p">(</span><span class="s1">&#39;&#39;</span><span class="p">)</span>

<span class="c1"># Transform the results in a pandas dataframe for easy plotting</span>
<span class="n">columns</span> <span class="o">=</span> <span class="p">[</span>
    <span class="s1">&#39;Stopping criterion&#39;</span><span class="p">,</span> <span class="s1">&#39;max_iter&#39;</span><span class="p">,</span> <span class="s1">&#39;Fit time (sec)&#39;</span><span class="p">,</span> <span class="s1">&#39;n_iter_&#39;</span><span class="p">,</span>
    <span class="s1">&#39;Train score&#39;</span><span class="p">,</span> <span class="s1">&#39;Test score&#39;</span>
<span class="p">]</span>
<span class="n">results_df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">results</span><span class="p">,</span> <span class="n">columns</span><span class="o">=</span><span class="n">columns</span><span class="p">)</span>

<span class="c1"># Define what to plot (x_axis, y_axis)</span>
<span class="n">lines</span> <span class="o">=</span> <span class="s1">&#39;Stopping criterion&#39;</span>
<span class="n">plot_list</span> <span class="o">=</span> <span class="p">[</span>
    <span class="p">(</span><span class="s1">&#39;max_iter&#39;</span><span class="p">,</span> <span class="s1">&#39;Train score&#39;</span><span class="p">),</span>
    <span class="p">(</span><span class="s1">&#39;max_iter&#39;</span><span class="p">,</span> <span class="s1">&#39;Test score&#39;</span><span class="p">),</span>
    <span class="p">(</span><span class="s1">&#39;max_iter&#39;</span><span class="p">,</span> <span class="s1">&#39;n_iter_&#39;</span><span class="p">),</span>
    <span class="p">(</span><span class="s1">&#39;max_iter&#39;</span><span class="p">,</span> <span class="s1">&#39;Fit time (sec)&#39;</span><span class="p">),</span>
<span class="p">]</span>

<span class="n">nrows</span> <span class="o">=</span> <span class="mi">2</span>
<span class="n">ncols</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ceil</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">plot_list</span><span class="p">)</span> <span class="o">/</span> <span class="mf">2.</span><span class="p">))</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">nrows</span><span class="o">=</span><span class="n">nrows</span><span class="p">,</span> <span class="n">ncols</span><span class="o">=</span><span class="n">ncols</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">6</span> <span class="o">*</span> <span class="n">ncols</span><span class="p">,</span>
                                                            <span class="mi">4</span> <span class="o">*</span> <span class="n">nrows</span><span class="p">))</span>
<span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">get_shared_y_axes</span><span class="p">()</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>

<span class="k">for</span> <span class="n">ax</span><span class="p">,</span> <span class="p">(</span><span class="n">x_axis</span><span class="p">,</span> <span class="n">y_axis</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">axes</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">plot_list</span><span class="p">):</span>
    <span class="k">for</span> <span class="n">criterion</span><span class="p">,</span> <span class="n">group_df</span> <span class="ow">in</span> <span class="n">results_df</span><span class="o">.</span><span class="n">groupby</span><span class="p">(</span><span class="n">lines</span><span class="p">):</span>
        <span class="n">group_df</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="n">x_axis</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="n">y_axis</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="n">criterion</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">)</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">y_axis</span><span class="p">)</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="n">lines</span><span class="p">)</span>

<span class="n">fig</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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